Dyfed-Powys Police said they received a report concerning the safety of a man last seen swimming in the River Wye at Glasbury.
The body of Lord David Lipsey, 77, was recovered on 1 July, after a search involving multiple agencies.
The village where it happened, in Powys, mid Wales, has a population of around 1,000 people.
Lord Lipsey’s next of kin have been informed and have asked for their privacy to be respected.
Police said in a statement that the force’s thoughts were with them.
Lord Lipsey became a member of the House of Lords in 1999 and has sat on the Labour benches for the majority of that period.
He was a long-time campaigner for water quality in the River Wye and his last spoken contribution in the House of Lords was on the subject.
He told the Lords that he and his wife had lived in the Wye valley “for nearly 30 years”.
“We go swimming at Glasbury most mornings in summer, some mornings in winter,” he said.
“We still do this, but it is a deteriorating experience. Part of the river near us was closed this summer to wild swimmers such as us, on the grounds of pollution.”
Prior to joining the Lords, Lord Lipsey worked as a journalist for a number of publications.
He later worked as a political adviser to the Labour Party in opposition and advised James Callaghan when he was prime minister.
The Lord Speaker said the House of Lords extended its “condolences to the noble Lord’s family and friends”.
